Steklov Institute of Mathematics at St.Petersburg

PREPRINT 10/2006

SUBGROUP SCHEMES OF A REDUCTIVE GROUP CONTAINING A SPLIT MAXIMAL TORUS

This preprint was accepted May 20, 2006

ABSTRACT:
In the previous paper, we classified all connected subgroup schemes
of a~reductive group, that contain a~split maximal torus,
over an arbitrary field. In the present paper we study the normalizer of
the subgroup schemes as above and classify all (not necessarily connected)
intermediate subgroup schemes.
The answer is given in terms of functions on the root system and
subgroups of the Weyl group.
We also describe the lattice of intermediate
subgroup schemes.